Sometimes people say that water is 9( ;*nxxfbvmg u m.ykgl(a5+wremoved from clothes in a spin dryer by centrifugal force throwing the water ou+(xgknbm 5(l; au gyv. fx9*mwtward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp cccj )p,c7ooa+ j/cas(urve at a constant 60 km/h cc+7jas)(/ oc ap,ojc as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed al3an/ ;bhpu3uwpj,ekr51g qz 3 ong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill/gj kb3 paqzr ; ewh3u3p51u,n, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a m.,gn zo+qnh3child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the c+z,.g nmohqn3 hild?

A bucket of water can be whirled in a vertiqp aqpkkfh 71-2b9pq3eh+p(qcal circle without the water spilling out, even at the top ofk7+3k9phae-q(qhp pbq2 qp1 f the circle when the bucket is upside down. Explain.

How many “accelerators” do you have mf/v+fv x2q,3pnpk8f in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do tkpm 2f +8xnv3pf/f ,qvhey produce?

A child on a sled comez5(:e h -ru0og0tbnles flying over the crest of a small hill, as shown in Fig. 5–31. His sled doeshn -0rb5o e(t:0lu zge not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at1:qywv r2fhn yz98j g5hk0b*q high speed?

Why do airplanes bank when they turn? How would y(; ht4 ,swksf; 0auuvrjkb j*7ou compute the banking angle given its speed kwsbhj ,0t(uakjfu ;sv ;4*7 rand radius of the turn?

A girl is whirling a ball on a string around her head in /cpr.q;kw-;/,vs sag(p g kyva horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. (wag.v;kpsy,vp/ k -;c/ rgsq When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, bvl imck3 p553how large a force? Consider an applei5lb3 vkcmp 53
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wa a 9oc4q6, d.*sujm mo6iwf n+fc2izl+ys would the Moon’s orbit b ,mlji+a.mn64ozc 2d 6 uf9qws*+icfoe different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E cc/u)nrp94 zfarth? Whic )4cfpzcu n9/rh accelerates more?

The Sun's gravitational pull on thdtp+;xbxj7i gx si c90.*s)ile Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from ong.x* blsx )ti+p9; 0diixc j7se side of the Earth to the other.]

Will an object weigh more at the equator or at tg t*a f suh0,zlp-)z4xnuv*g u*.b sg6he poles? What two effects are at work? D)g4v aupft** 6gz0*-,usg. uzsxlhn bo they oppose each other?

The gravitational force on the Moon due to the Earth is only about hal/9l orupyqr 4;f the force on the Moon due to the Sun. Why isn’t the Moo; uq 49r/rlypon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbi0 od+u0 xo+ man*m6xa hjd))fnt around the Sun larger or smaller thm)nuonax*+md6 0 +)f ax0h djoan the centripetal acceleration of the Earth?

Would it require less speed to launl*j-oa xg5 qpx7:gb - (,,kgkxb3zyujch a satellite (a) toward the east or (b) toward the west? Consider the Exak-*:k7ugqz j5(o - gpxj g,bbx3,y larth’s rotation direction.

When will your apparent weighknzunt;7r -3j t be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When wj-t un7;rn3kzould it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely t1he0 1uwoh y/y1.0dagfd c2ua+ugr 0affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and 0uu .au oyhd ryg1/fg a+01wchd102te(c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightld*z; l*7opcgpwt-k*p(2mf(ymux ;j d essness” between *-pmpkz*;c;u (7dx2j o ypmwg f *dtl(steps.

The Earth moves faster in its ;yfw84 8)f iy9ta2p dd0w4zcgqv 8pf eorbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing thepc 9dy8ytg4ffa4 dvw28) 8z e qipf0w; seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known unozf womw1))3(h q szd)til it was discovered to have a moon. Explain how this discovery enabled an estima))mz zf(s1wo )3who qdte of Pluto’s mass.

  The Sun's gravitational pull on the ig/fnn7 3f2p pdcb91vEarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.vfn7p/bf 1id 3c9n2gp25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980-0wcg 4r1kpf z $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around thc ba,tkmro;/, e Sun, and the net force exerted on the Earth. What exerts th o/,c;ba rt,mkis force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-k n4deiel;k; g8en 2 ed:,r;uatg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculatln ;; 2dtue4kera,nid:e;g8e e the speed of the discus.   

  Suppose the space shuttlmaq5 org6p9,8tovv) m7dd t 0de is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minu t7 )68o5vm,ddtdq9rag p0mvotes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration cyd9;ol1b gk jw-h hg*e4m )s3of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minuge;csw*-y9 4gholh 3jm1 d k)bte) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a v.efhu 9ytu no:ee, p *e0txvun on:)+8ertical circle of radius 72.0 cm ,.:oee u):,epno* 98e0unnttf +xhyvu as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum sp0f yw e5xv5nk7eed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction 05e vxywn 5kf7between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficiep qpr-f*mr h 9g7fd8x3nt of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a spee 8* -qpxdfrmr7 hp9fg3d of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a h.pc :i90kg6j 8wy/t ulwd yv1trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotatidj8wthylyv.g/ 9:p0 1 c w6kuing?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable 5b-0gu.f mnbdyja(-zspeed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until amjbab f-yd.5-nuzg 0 ( rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed hazdp*q bei9ia0;vn b ;o)) n3must a roller coaster be traveling when upside down at the top of a circlz0 qab93nb; aih *)dpen;i)voe
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass u bve xnvg 7.6g+w9iv+950 kg (including the driver) crosses the rounded top of a h+gu. ge9bvvinv7x +6will (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions56z sc 799cuo8sou sal per minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at 9sol9 zcu56su8 sco7a the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad q7(brsap(k5;jl hlfvxi6/ / bius 1.10 m. At the lowest point of its motion the tension in the rope supporting the b q//ls(r5v(f ;xip 6hlbjab7kucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge roxin, 2yn7t(cy tate if a particle 9.00 cm from the axis of rotation is to experience an acceleratio7 nnytx2i (y,cn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wallediws2 ++uv8jwm.pn h g5 "room." (See Fig. 5-35.mg. 25 vun8 wswhp++ji)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle onpa pi.bq zm 7tle3oh :inw.2-7 a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cem77.qw .ti 3i aze-o hp:2bpnlntral hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight 3qv9dh i ,5sn*6wdgfzir/. kmof the ball which revolves on a string zk*vimnrqh./f3w d gid,59s60.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveiqts.r+:hu/r ling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses 1f g;w iiwhidy 6w;6/gvai2u3$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertica9dta km:d 9i 9x;eeym(lly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and cejkbav5lz )q 7po :jo.r7;(sc7m;rc nuntripetal components of the net force exerted on the car (by the ground) in Examplmcj;p o:.r rjaoc(v)b;uk qz7s77n l 5e 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unig6 : p3 hsf8ds8v7kfzaformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provi87z fsafpg8dk6v 3s h:de this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pa.,x rvqq bp((0mngte7 rticular instant, its.qb(, v ep07 rqnmgtx( acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravib3)di 4 ++ e;xsvzynvzn33qg pty on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mas;3n+)d z 4x y3zisgb+vvenpq 3s is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has,eepa cm5 qrm3-eh4 :o a magnitude of 12 m/sh pmo3ra-,c45: q emee$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on thjlugc ;b0m- 7 nw:jj7. scklf;e Moon. The Moon's radius is 1.7 07sc:lb7 k.jj c;ul-;fwmj gn4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times thatikamflw30 vnp5,2w964 pmbi w rd/m1s of Earth, but has the same mass. What is the acceleration due to gravity4sl 2ndwi bv5f,wpm3p6/kami0wr9m1 near its surface?   

  A hypothetical planet2var)fifn m b15k **bf,8hw bg has a mass 1.66 times that of Earth, but the same radius. What is g2ikr 51f8fh*,wabfgn*) vmb b near its surface?   

  Two objects attract each other gravitationaly 6z;s:vnyac0d/tth9w8 0t1 d vpefo3g,hs.nly with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravitpkfptg :0 2lwra*u8k -igyh 9,y, at (a) 3200 m 0-p2 ailgyhf9r kt up 8k,g:*w   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outh j*hzzyd t0d *s(ul jqij2eaz32/2 2zside the Earth where thegravitation ji2sz 3d (*u*z2 yjhqlzz2 2/0ahtjedal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the ir1m c,;m6:ikf:vak y mass of our Sun packed into a sphere about 10,1i;fvc6mam :k ry:ki km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averah *2z8hq r.bqjge star like our Sun but is now in the last stage of its evolution, isqb *r.8hh zqj2 the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why kbd7da-y;b jim/i g d3wce -v;8bc4x/astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Eartgx/8 7;vbibayi;- c w-cdd 4k d/3jembh’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m u+kz8 m8rx)wm. Calculate the magnitude and direction of the total gravitational force exerted on one sphere 8kwxmr z8 )m+uby the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of theum oxi ;f w2bi(14pmj/(9 jxge planets line up on the same side of the Sun. Calculate the total force on the Ear1 m 2ow9(ijm gujie xpfb/4x(;th due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleo2fsw7*mz 4s7n i)yz cration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Ma 2 c*zzoi7s7y) nws4fmrs.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuv+mmct -rvreu 27ax, ;e for the period of the Earth and its distance from th+e7mx -ut,r;a vv 2rmce Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cmr lrnfp, c:;jbu*6r0ircular orbit about the Earth at a he;pr mflu:jbr,r*60c night of 3600 km.    $\times 10^3$

  The space shuttle releases a sl aok rnx+-b 18p8rsa+atellite into a circular orbit 650 km above the Earth. How a88rra+oslx-pn b +k1 fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotapdn)ajo:3u 0vk tsy:kn1 0q29w ,vfo cte if occupants are to experience simulated gravitkv)adcf2y0o 10povk 9nus3t wn, ::jqy of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Eartb2bxi6) v ao9gh in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small comparvoag2i9 b6x)b ed to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from th cshj1+s(v( w9p17le.aakadh e top of Mt. Everest to be placed in a(v+1dl a1ws (sp9j7c ha kha.e circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cont,s7*xu bk8v x-rz)yyhinued to orbit the Moon at an altitude of about 100xy)v8sy,r zbku7 -x*h km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the prvp2f5cax1sw2 1l ;eplanet. The inner radius olca1 21 rwx2pf5;veps f the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–f q f 5.z dye2/.k3prpdv8fns49). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at thefp .3r/58d2k 4ze.vy ndqpsff bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrokvvngb38z42ae5qy x4naut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocitye4bykz g358a4n q v2xv,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. The tdmx..vu)my3 y are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them.ym 3. )dmvxt.u What is the mass of each?    $\times 10^{29}$

  What will a spring scan kl +/3s8o9lzocl7omle read for the weight of a 55-kg woman in an elevator that moves l+zk8 /lls3o9o7cnmo
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. Tmz fos6 g0y8e:he cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directi:fge mz0sy86o on)? a =   

Show that if a satellite orbits very0m-,f98venuwf pfg)b near the surface of a planet with period T , the density 9wgub)fv8mfne-0 ,pf (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determi q) cso x n6a+t.r2+s8qxfhu2mne the period of an artificial satellite orbiting very near the Earth’s .2 +fu)qsr txh2nqox+s86cm a surface.    s

  The asteroid Icarus, though only a few hundred meters a:pehv(o+ gf c.cross, orbits the Sun like the planets. Its period is 410 d. What is its mean distance .:h +e pvgocf(from the Sun?    $\times 10^{11}$

  Neptune is an average distance of u8lf)3v )i zbeqt20n x4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. 0e gp .ry6uprsyk) q71y5xo4 oIt comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in 40o1y7soyup ) r.gkqe r yxp56Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy0 w(c6q3j ;xrr;j *0qruftxhu $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons ox(5 wn)sig1 yq r;t(gkf Jupiter (those discovered by Galileo in 1609)5riy( w)gq1 g(;tsx nk.
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of tl //+h,f7osodg qh52p7hfok yhe Earth from the known period and distance of the Moon. yd k7/2oh/f7gopl+,h sfoh5q    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usixq44/ 9n2n x xbi9eirhmesw)8 ng Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compaxi nhqex2sr8w) i4mnx/4e 9b 9re to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragme+9n/kz:msm 6ed8u a kqnts (which some space scientists think came from a planet that once orbited the uzmn+6a/ 9 k:e8m dksqSun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artink gu9cssfl/y ) l;,f)ficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. Whatl9lcgkf;/)n su ),yfs will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an aiz:wvkbotcaq8k/ 8 o kg p3jk6i)8(,arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowestk6pa ) jiz,bgckowk a3kiv(/8 88:oqt point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hi cndmjz((4+p alf what it d m((jc4+inpzis on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cgu4o,xo 8pmw: r.w1 y7 1;3thdxyfnrbircle once every 2.5 s. If we assume their arms are each 0.80 m long and their indiv h8py ryxu7n 1tb;x4rdf:wm,g w1o3.oidual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rot) :gtv. 2ctttbw. )1biwc ny1rates once per day, the apparent acceleration of gravity at the equator is slightly tby1) ir)c.g:wttnbt2 wc1 .vless than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a space6,tiq c-a8dg t:a2 oykcraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull wikaqo8,dt:t -iy 62g cath equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you sk3: h6cczwa 2ntand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directizkc 36:cahnw 2on?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abou.avg3 .dyv ku-t its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must yg .-u. dvka3vbe the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loopvi a g (5cdg out79cl6ej58aj5 (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in ter; n6gdhga,b1 vms of its radius r, the acceleration due to gravv a6gd;gh1b n,ity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) i:vi ik+d4xq2y rmz/ o2s deflected from the vertical by an an zm2o4kq:/iyx+rvid2 gle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If tha0x7d;t ef jni s7+-epe coefficient of static friction is 0.30 (wet pavement), ati0- 7ea+ tfdex;7pj sn what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth werez,ao3zyf)m4 j rotating so fast that objects at the equator were appa zjza4, oy)f3mrently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a rfa*o : j,zv8xibij9-constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius jx o38m9)jw2 .ejh nmb235 m. A lamp suspended from the ceiling swings out to 2.jh neo)j8xmm3wb9j an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as magbo2wh9 e bsa8- 7u:ztssive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't bu9was:z hgbo 7e 2-8tsurvive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Tepzu2rd(e:, t ;p.otmulescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black holropd2zmt ;:(,p e.uu te (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a consta qg*y7hdb.6mh:snx 5. u +fwobnt speed as it traverses the hill and valley shown in Fig. 5–45.+o:u hgfb*q.n7sh5m 6dxw b y. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positionwkowytip8 5b) 4 x8ve3ing System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within anp84 wyv5wx8eko 3ibt ) accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous kgsx,g sv 1of6s)ft 7rcf,fy +c.7jy4(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abo ofg +y4c67y)vfxrs7tf,ks1. jfs cg,ut 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite isp)dlsg. /mvpt0t2+ds gg3j3,wp- h en need of repair. You are in a circular orbit of the same radius 3s0p2)pl g-gv3ws,mdegdp+ j s t/th. as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a pcme8gwyfuwpx+ 09)s 6.j1 mwog+ +pkleriod of 3000 years. (a) What is its mean distance from eo u+)m1. 0+wpxgp9c g fyk6l mswj8+wthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G wors*z2c8p bknksd(*:kuld need to be if you could actually "feel" yourself gravitaps:snr**( 82d k kbckztionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of aakb*) 5uwe*: ovtp) 8eapeo( the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from t(p e5wo*)aoaetaku) pbv *e 8:he center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are loca4w3r9 socf: mxted at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sidr3o4 w9m csf:xe of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5j 0 ; fo-ahnz em9z/992pjj (flvnzw;m500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep dia(9xd). uz,y) .*ebwx ygl msecond hand on your,idy xaz*9e(m wugdb .)y)lx . wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a si a*adb*f mi00l. s)bphnker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle s d bl 0i0fpab*)am.h*that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed soo r ziiyj:f,i )pj3l0+d(jnv2 n-,uyo that a car traveling aty ,rjy -njdo3 o2+)j (iin0ipflvuz,: speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whe()q sb:0/hn z mpxh8jen negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feelingq(h/hbx pj8n0se) z:m more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$